Statistics of Transverse Velocity Differences in Turbulence

An unusual symmetry of the equation for the generating function of transverse velocity differences $\Delta v=v(x+r)-v(x)$ is used to obtain a closed equation for the probability density function $P(\Delta v,r)$ in strong three-dimensional turbulence. It is shown that the terms, mixing longitudinal and transverse components of velocity field, dominate the pressure contributions. The dissipation terms are closed on qualitative grounds. The resulting equation gives the shape of the pdf, anomalous scaling exponents and amplitudes of the moments of transversevelocity differences.